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      【ARC072F】Dam
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        <p>首先明确一点，每天的水不管你觉得它好不好，你都得接下它</p>
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<p>假如现在需要放出x升，并且L升之前的那个水u，它后面有一个比它温度更大的水v，显然是放掉u的x升。那假如v的温度比u更小，你是选择在v进来之前放掉u的x升，还是等v进来之后再放x升呢？傻子都知道等v进来再放！根据热量守恒定理，你的总热量是不变的，而同样失去x升水，肯定放出温度小的热量损失更小。</p>
<p>于是我们就可以用单调递增队列来做了！队列里将最后那L升水分成若干份存储，满足温度递增，假如有哪个水的温度比前面那个小，那就把它们混合起来（直接套题目给的公式）</p>
<p>然后每进来一盆水就把它丢进队尾，并维护一遍单调队列，顺便计算答案。答案很好统计，只要随时记录队列中各个水的温度与体积的乘积之和，答案就用它除以L就是了</p>
<p>复杂度是O(n)的，瓶颈在于IO，我凭借fread/fwrite成功跑进了100ms。不过话说网上怎么搜不到浮点数快输的板子，搞得我还自己手写了一遍，嗯以后可以存着用了</p>
<div class="highlight-box" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false" contenteditable="true" data-rel="CPP"><figure class="iseeu highlight /cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span 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class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span><span class="meta-string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> FR first</span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">define</span> SE second</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"></span><br><span class="line"><span class="keyword">const</span> <span class="keyword">int</span> S=(<span class="number">1</span>&lt;&lt;<span class="number">20</span>)+<span class="number">5</span>;</span><br><span class="line"><span class="keyword">char</span> buf[S],*H,*T;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="keyword">char</span> <span class="title">Get</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(H==T) T=(H=buf)+fread(buf,<span class="number">1</span>,S,<span class="built_in">stdin</span>);</span><br><span class="line">    <span class="keyword">if</span>(H==T) <span class="keyword">return</span> <span class="number">-1</span>;<span class="keyword">return</span> *H++;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="keyword">int</span> <span class="title">read</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">int</span> x=<span class="number">0</span>;<span class="keyword">char</span> c=Get();</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isdigit</span>(c)) c=Get();</span><br><span class="line">    <span class="keyword">while</span>(<span class="built_in">isdigit</span>(c)) x=x*<span class="number">10</span>+c-<span class="string">'0'</span>,c=Get();</span><br><span class="line">    <span class="keyword">return</span> x;</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">char</span> obuf[S],*oS=obuf,*oT=oS+S<span class="number">-1</span>,c,qu[<span class="number">55</span>];<span class="keyword">int</span> qr;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="keyword">void</span> <span class="title">flush</span><span class="params">()</span></span>&#123;fwrite(obuf,<span class="number">1</span>,oS-obuf,<span class="built_in">stdout</span>);oS=obuf;&#125;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="keyword">void</span> <span class="title">putc</span><span class="params">(<span class="keyword">char</span> x)</span></span>&#123;*oS++ =x;<span class="keyword">if</span>(oS==oT) flush();&#125;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="keyword">void</span> <span class="title">printd</span><span class="params">(<span class="keyword">int</span> d,<span class="keyword">double</span> x)</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">long</span> <span class="keyword">long</span> t=(<span class="keyword">long</span> <span class="keyword">long</span>)<span class="built_in">floor</span>(x),f=t;</span><br><span class="line">    <span class="keyword">while</span>(t) qu[++qr]=t%<span class="number">10</span>,t/=<span class="number">10</span>;</span><br><span class="line">    <span class="keyword">while</span>(qr) putc(qu[qr--]+<span class="string">'0'</span>);</span><br><span class="line">    putc(<span class="string">'.'</span>);x-=f;</span><br><span class="line">    <span class="keyword">while</span>(d--)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">double</span> y=x*<span class="number">10</span>;x*=<span class="number">10</span>;</span><br><span class="line">        <span class="keyword">int</span> c=(<span class="keyword">int</span>)<span class="built_in">floor</span>(y);</span><br><span class="line">        putc(c+<span class="string">'0'</span>);x-=c;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">long</span> LL;</span><br><span class="line"><span class="keyword">typedef</span> pair&lt;LL,<span class="keyword">double</span>&gt; pld;</span><br><span class="line"><span class="keyword">const</span> <span class="keyword">int</span> N=<span class="number">500010</span>;</span><br><span class="line">LL t[N],v[N];</span><br><span class="line">pld q[N];</span><br><span class="line"><span class="keyword">int</span> l=<span class="number">1</span>,r=<span class="number">0</span>;</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">    <span class="keyword">int</span> n=read(),L=read();</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">        t[i]=read(),v[i]=read();</span><br><span class="line">    <span class="keyword">int</span> sum=<span class="number">0</span>;<span class="keyword">double</span> cur=<span class="number">0</span>;</span><br><span class="line">    <span class="keyword">for</span>(<span class="keyword">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">    &#123;</span><br><span class="line">        <span class="keyword">while</span>(v[i]+sum&gt;L)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="keyword">int</span> pour=min(v[i]+sum-L,q[l].FR);</span><br><span class="line">            sum-=pour;</span><br><span class="line">            q[l].FR-=pour;</span><br><span class="line">            cur-=q[l].SE*pour;</span><br><span class="line">            <span class="keyword">if</span>(!q[l].FR) l++;</span><br><span class="line">        &#125;</span><br><span class="line">        q[++r]=pld(v[i],t[i]);</span><br><span class="line">        sum+=v[i];cur+=<span class="number">1l</span>l*t[i]*v[i];</span><br><span class="line">        <span class="keyword">while</span>(l&lt;r&amp;&amp;q[r].SE&lt;q[r<span class="number">-1</span>].SE)</span><br><span class="line">        &#123;</span><br><span class="line">            q[r<span class="number">-1</span>].SE=(q[r<span class="number">-1</span>].SE*q[r<span class="number">-1</span>].FR+q[r].SE*q[r].FR)/(q[r<span class="number">-1</span>].FR+q[r].FR);</span><br><span class="line">            q[r<span class="number">-1</span>].FR+=q[r].FR;r--;</span><br><span class="line">        &#125;</span><br><span class="line">        printd(<span class="number">7</span>,cur/L);putc(<span class="string">'\n'</span>);</span><br><span class="line">    &#125;</span><br><span class="line">    flush();</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure></div>

      
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